Math Word Problems?

Question

1. The Length of a rectangular cement patio is 3 ft less than three times the width. The sum of the length and the width of the patio is 21 ft. Find the length of the patio.

2. A coin bank contains pennies, nickels, and dimes. There are six times as many nickels as pennies and four times as many dimes as pennies. The total amount of money in the bank is $7.81. Find the number of pennies in the bank.

Answer 1

Patio Problem

Let L be the length and W the width.

"The length of a rectangular cement patio is 3 ft less than three times the width."

L + 3 = 3W

"The sum of the length and the width of the patio is 21 ft."

L + W = 32

Use the first equation to get an expression for L and substitute into the second...

( 3W - 3 ) + W = 32

4W = 35

W = 8.75 and L = 23.25

Coin Problem:

Let P, N, and D be the numbers of pennies, nickels, and dimes.

"There are six times as many nickels as pennies..."

N = 6P

"and four times as many dimes as pennies."

D = 4P

"The total amount of money in the bank is $7.81."

( .10 ) D + ( .05 ) N + ( .01 ) P = 7.81

Substitute the first two expressions into the third...

( .10 ) 4P + ( .05 ) 6P + ( .01 ) P = 7.81
.40 P + .30 P + .01 P = 7.81
.71 P = 7.81
P = 11

There are eleven pennies, sixty-six nickels, and forty-four dimes.

Answer 2

1: length = 3x - 3 = 3(6) - 3 = 15
Width = x = 6
L+w = 21

3x-3 + x = 21
4x = 24
x = 6

Check = 6 + 15 = 21 yes works :)